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(abridged) Context: Turbulent diffusion of large-scale flows and magneticfields play major roles in many astrophysical systems. Aims: Our goal is tocompute turbulent viscosity and magnetic diffusivity, relevant for diffusinglarge-scale flows and magnetic fields, respectively, and their ratio, theturbulent magnetic Prandtl number, ${\rm Pm}_{\rm t}$, for isotropically forcedhomogeneous turbulence. Methods: We use simulations of forced turbulence infully periodic cubes composed of isothermal gas with an imposed large-scalesinusoidal shear flow. Turbulent viscosity is computed either from theresulting Reynolds stress or from the decay rate of the large-scale flow.Turbulent magnetic diffusivity is computed using the test-field method. Thescale dependence of the coefficients is studied by varying the wavenumber ofthe imposed sinusoidal shear and test fields. Results: We find that turbulentviscosity and magnetic diffusivity are in general of the same order ofmagnitude. Furthermore, the turbulent viscosity depends on the fluid Reynoldsnumber (${\rm Re}$) and scale separation ratio of turbulence. The scaledependence of the turbulent viscosity is found to be well approximated by aLorentzian. The results for the turbulent transport coefficients appear toconverge at sufficiently high values of ${\rm Re}$ and the scale separationratio. However, a weak decreasing trend is found even at the largest values of${\rm Re}$. The turbulent magnetic Prandtl number converges to a value that isslightly below unity for large ${\rm Re}$ whereas for small ${\rm Re}$, we findvalues between 0.5 and 0.6. Conclusions: The turbulent magnetic diffusivity isin general consistently higher than the turbulent viscosity. The actual valueof ${\rm Pm}_{\rm t}$ found from the simulations ($\approx0.9\ldots0.95$) atlarge ${\rm Re}$ and scale separation ratio is higher than any of the analyticpredictions.

Turbulent viscosity and effective magnetic Prandtl number from simulations of isotropically forced turbulence